An Analysis on Instantaneous Stability of an Associative Chaotic Neural Network.

We analyze instantaneous stability of a chaotic neural network which shows nonperiodic associative dynamics. The network is composed of discrete-time neuron models of which individuals show chaotic dynamics with certain parameter values. The synaptic weights of the network are determined by an auto-associative matrix so that four binary patterns are stored as a basal memory of the network. It has been reported that the network retrieves stored patterns nonperiodically. However, the dynamical property of the network in each discrete-time step has not been clarified. In this paper, instantaneous stability of the network during the nonperiodic memory retrieval is analyzed by calculating eigenvalues of the Jacobian matrix. From the analysis, it is found that in every instance when the network retrieves stored patterns, all the eigenvalues are always less than unity. This implies that such states of the memory retrieval cannot be a target of the OGY-like chaos control methods. [ABSTRACT FROM AUTHOR]